Creating a working democracy in Iraq would be a "huge blow" to the propaganda of extremists and terrorists, Tony Blair told the BBC.
Mr Blair and Mr Bush say Mid East peace roadmap not "annihilated"
He said most Iraqis wanted to see a democratically-elected government.
And he insisted Israeli plans to retain Jewish settlements in the West Bank did not "annihilate" the "roadmap" for Middle East peace.
Mr Blair spoke to Radio Four's Today programme after he and George Bush showed solidarity at a US summit.
He said he felt "total resolve and determination" about the 30 June handover of power in Iraq.
The prime minister said it was "our job" to make sure the "fanatics" in Iraq did not win.
Whatever their beliefs were about going to war in Iraq, people should realise there are now two sides to choose from, he said.
"On one side are the fanatics extremists and terrorists.
"On the other side are the Iraqi people - the vast majority of them - those decent people you meet at the Iraqi Governing Council, the UN, the coalition, and any country that wants to see Iraq become stable.
"In those circumstances there's only one side to be on," he said.
Mr Blair has returned to the UK from the US where he also held talks with UN Secretary General Kofi Annan.
In an interview with the BBC before he left Washington, he said "terrorists, extremists and fanatics" wanted to see "progress halted" in Iraq.
The "vast majority of Iraqi people" wanted to see their country run as "a broad-based, secular government, democratically elected."
"We have to do what it takes to see it through and get it done," he continued.
Violence in Iraq meant the coalition had to run the campaign as a "hearts and minds" as well as military operation.
"In the end there is a big, big choice facing the world on security and terrorism.
"We can either back away and let this threat develop even after the warnings we've had or we can try and stop it."
He said September 11 had been a defining moment because it had given a sense of urgency to dealing with this new security threat.
His comments came after he and Mr Bush together vowed not to waver in their fight to build a free Iraq.
At the White House on Friday they said they would keep their promise to the Iraqi people and "get the job done".
UN 'central role'
The summit followed Mr Bush's support for Israeli Prime Minister Ariel Sharon's plan to unilaterally withdraw from Palestinian land in the Gaza Strip, but retain settlements built in the West Bank in defiance of international law.
Mr Blair told the BBC he was "realistic" about the Middle East peace saying Mr Sharon's plan gave an "opportunity to get back into the road map process".
On Friday, Mr Bush said he and Mr Blair did not believe Mr Sharon's plan prejudged talks on a final settlement.
In Washington, Mr Blair underlined the need for the United Nations to have a "central role" in moving towards the power transition saying he hoped there would be a new Security Council resolution over Iraq.
Meanwhile senior US officials said they were prepared to accept a plan by UN special envoy Lakhdar Brahimi that proposes replacing the US-appointed Iraqi Governing Council by a caretaker government after 30 June.
This would run Iraq until elections could be held.
Its leaders would be chosen by the UN after consultations with the US, the Governing Council and other Iraqis.